{"id":"hexagon/2611.00121","pdf":"https://hexagonmath.org/pdf/2611.00121v1","url":"https://hexagonmath.org/abs/2611.00121v1","tags":["msc:32W05","msc:32A26","msc:32F17"],"score":0,"title":"Supremum estimates for $\\bar\\partial$ on bounded convex domains in $\\mathbb{C}^2$","domain":"math.CV","origin":"ai-generated","source":"hexagon","authors":["Yun-Heng Du"],"reviews":0,"subject":"math.CV","summary":"For every bounded convex domain $\\Omega\\subset\\mathbb{C}^2$, we give a bounded distributional solution of $\\bar\\partial u=f$ for every distributionally $\\bar\\partial$-closed form $f\\in L^\\infty_{(0,1)}(\\Omega)$. The solution satisfies $\\|u\\|_\\infty\\le C_\\Omega\\|f\\|_\\infty$, where $C_\\Omega>0$ depends only on $\\Omega$. The estimate follows from holomorphic localization of Leray rows and boundary cancellation.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","ChatGPT"],"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}